The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane 2x - y = 1. The resulting intersection is a curve on the surface. Find a set of parametric equations for the line tangent to this curve at the point (1,1,-23/24).

a. For which of these projects is the IRR rule​ reliable?

The IRR rule is reliable for (project 2 /project 3 /project 1) Unless all of the (positive/negative) cash flows of the project precede the (positive/negative)

ones, the IRR rule may give the wrong answer and should not be used.​ Furthermore, there may be multiple IRRs or the IRR may not exist.

b. Estimate the IRR for each project​ (to the nearest

1%​).

c. What is the NPV of each project if the cost of capital is

5%​?

20%​?

50%​?

A firm called AstraZeneca uses labor and machines to produce output according to theproduction function ?(?,?)=4?^1/2?^1/2 where ? is the number of units of labor used and ? is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10.

(a) On a graph, draw an isocostline for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. What is the slope of these isocost lines?

(b) Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker.

(c) On a graph, sketch the production isoquant corresponding to an output of 40. Calculate the amount of labor and the number of machines that are used to produce 40 units of output in the cheapest possible way, given the above factor prices. Calculate the cost of producing 40 units at these factor prices.

(d) How many units of labor and how many machines would the firm use to produce y units in the cheapest possible way? How much would this cost?

Perform a linear time series regression (“Trend Analysis” in Minitab or “Trendline” in Excel) of the historical data. For the parts below, generate a regression output report produced in either Excel or Minitab and submit it with your completed test.

a.   Attach a copy of your “Trend Analysis” or “Trendline” graph in a space created BELOW.

b.   State (here) the equation of the fitted regression line.

c.   On the basis of this regression analysis, calculate and state numerical values of the sales revenue forecasts for all four quarters of 2018.

d.   Calculate and state (here) the RMSE of this simple linear regression. [Hint: Different from forecasting, for regression RMSE = √SSE/√(n-2).]

The table represent a random sample of 31 test scores taken from a large lecture class. Find the following [round to 2 decimal points X. XX]

a) [2 pts] Find the 5 number summary [L, Q1, Q2, Q3, H]

b) [4 pts] Find the mean and standard deviation.

c) [2 pts] Find the IQR

d) [2 pts] Are there any outliers in the test scores? Explain

e)[ 1 pt] Suppose one student in the sample is randomly selected. What is the probability that this student scored less than 50 [leave as a fraction]

State the method ( Winter's additive or multiplicative) which is the most accurate to forecast for 2018 according to the data set?

With the above data, could you please help me answer the questions below.

Type or paste question here

With the above data, could you please help me answer the questions below.

With the above data, could you please help me answer questions 10-13:

Calculate a 95% confidence interval for the mean mileage of make 2. Use the method for single means when σ is not known, but use the Error Mean Square as the estimate of the variance. The degrees of freedom will be the Error DF, not n-1!

Reminders: Confidence Interval = mean ± margin of error Margin of error = critical value * standard error Use critical value for T at α/2 = 0.025 and df = error df (t table or EXCEL T.INV function) Use standard error = √(error mean square/number of observations of that make of car)

10. What was the margin of error for the confidence interval for gasoline mileage of make 2?

11. What was the lower 95% confidence limit for make 2 mileage?

12. What was the upper 95% confidence limit for make 2 mileage?

Conduct a test of the hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not known with the Error MS serving as the pooled variance.

Reminders: Test statistic t = difference of means / standard error of difference of means. The standard error of the difference equals square root of the sum of variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean.

13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?